Module MATH43220: Bayesian Statistics

Department: Mathematical Sciences

MATH43220: Bayesian Statistics

Prerequisites

• Statistical Concepts

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide an overview of the theory and practice of Bayesian inference and Bayesian statistical modelling.

Content

• Foundations of Bayesian modelling and inference: rationality, exchangeability, sufficiency, conjugacy.
• Bayesian statistical modelling: hierarchical models, Bayesian networks, conditional independence.
• Computation for Bayesian inference: Monte Carlo, Markov chain Monte Carlo, Gibbs sampling, Metropolis-Hastings.
• Practicalities in Bayesian inference: prior distributions, interpretation and analysis of MCMC output, model comparison.
• Reading material in an advanced area of Bayesian statistics chosen by the lecturer.

Learning Outcomes

• Awareness of a wide range of aspects of Bayesian statistics.
• A systematic and coherent understanding of the theory, computation and application of the mathematics underlying the Bayesian approach to statistics.
• Have acquired a coherent body of knowledge about the theoretical foundations underpinning the application of Bayesian statistical inference to scientific and other problems.
• Have acquired a coherent body of knowledge about the practical application of Bayesian statistical methods.
• Knowledge and understanding obtained by independent study of a substantial topic in an advanced area of Bayesian statistics.

• In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling, Computation.

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Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University